1. Field of the Invention
The present invention relates to a lenticular lens sheet for use as a rear-projection screen for a projection television system in which light rays from a picture source are projected on a projection display screen on an enlarged scale by a lens system. More particularly, the present invention relates to a lenticular lens sheet for use as a rear-projection screen on which a picture produced by a single picture source, such as an LCD (liquid crystal display) or a DMD (digital micromirror device) is projected for observation.
2. Description of the Related Art
A known projection television system employs three picture sources, i.e., a red, a green and a blue CRT, enlarges pictures formed by the three picture sources by a projection lens system, and projects the enlarged pictures on a rear-projection screen. Liquid crystal projection television systems have been used in recent years instead of such projection television systems employing three CRTs. The liquid crystal projection television system employs three LCD panels, i.e., red, green and blue LCD panels, as picture sources, combines pictures formed by the three LCD panels by a dichroic mirror to form a composite picture, and displays the composite picture. The brightness and contrast of pictures produced by the current LCD are lower than those of pictures produced by a picture source comprising red, green and blue CRTs. Therefore, it is desired that an LCD rear-projection screen for displaying pictures produced by the LCD picture source is capable of displaying pictures in a contrast higher than that of pictures displayed on a CRT rear-projection screen for displaying pictures produced by the CRT picture source.
When a lenticular lens sheet provided with a light absorbing layer on its front surface, i.e., a surface on the side of viewers, is used as a rear-projection screen, a method which increases the black stripe ratio of the lenticular lens sheet, i.e., the ratio of the area of black stripes formed on the front surface of the lenticular lens sheet to that of the front surface of the lenticular lens sheet (hereinafter referred to as "BS ratio") is the most effective means for increasing the contrast of pictures displayed on the lenticular lens sheet. Generally, the LCD picture source is provided with a single LCD and, therefore, less light rays fall from oblique directions on the lenticular lens sheet when the LCD picture source is used than when the CRT picture source is used. Therefore the BS ratio of the lenticular lens sheet can easily be increased when the LCD picture source is used.
FIGS. 7A and 7B show a single-display lenticular lens sheet 1 for displaying pictures produced by a single-display picture source and a three-display lenticular lens sheet 1 for displaying pictures produced by a three-display picture source, respectively. Light rays emitted by a single-display picture source fall on the back surface of the lenticular lens sheet 1, i.e., a surface facing the picture source, more specifically, on a plane in contact with a plurality of lenticular lenses forming the back surface of the lenticular lens sheet 1, at incident angles about a specific angle as indicated by solid lines in FIG. 7A and hence a light absorbing layer 4 can be formed in a large BS ratio. Light rays emitted by the three displays of a three-display picture source fall on the back surface of the lenticular lens sheet 1 at incident angles about a plurality of different incident angles (only two different incident angles are shown in FIG. 7B) as indicated by solid lines and dotted lines in FIG. 7B and hence a light absorbing layer 4 cannot be formed in a large BS ratio to transmit the oblique incident light rays indicated by dotted lines.
Geometrically, an upper limit of the BS ratio is in the range of 50 to 55% if, for example, the oblique incident light rays indicated by dotted lines fall on the back surface of the lenticular lens sheet 1 at an incident angle of 10.degree.. Generally, the light absorbing layer 4 is formed on the surfaces of elevated sections 5 having a substantially rectangular cross section. If the elevated sections 5 have a great height, light rays leaving lenses 3 on the front surface of the lenticular lens sheet 1 are trapped by the elevated sections 5, so that the viewing angle of the lenticular lens sheet 1 is narrowed. A rear-projection screen proposed in JP 8-313865A for displaying pictures produced by an LCD or a DMD employs a Fresnel lens in diffusing projected light rays to reduce scintillation. Since light rays fall on the lenticular lens sheet at incident angles distributed in a certain range, the quantity of light which is not emitted by the lenticular lens sheet increases if the BS ratio is excessively large.
Generally, light rays leaving the Fresnel lens disposed on the back surface of the lenticular lens sheet are substantially parallel and are not exactly parallel. Therefore, light rays other than those falling on a central section of the lenticular lens sheet with respect to the width of the lenticular lens sheet fall obliquely on the lenticular lens sheet. Back lenses and front lenses are formed respectively on the back surface and the front surface of the lenticular lens sheet with an optical registration but with a geometrical positional difference between the back lens and the corresponding front lens, to transmit light rays efficiently. JP 59-69748A proposes a method of determining the positional difference d of the lenticular lens sheet by using the following expression: ##EQU1## where t is the thickness of the lenticular lens sheet, i.e., the distance between the respective surfaces of lenses on the back surface and lenses on the front surface, n is the refractive index of the material forming the lenticular lens sheet, r is the distance from the center, and f.sub.2 is the focal length of the Fresnel lens.
In a strict sense, this expression merely expresses the positional difference between a light ray leaving a Fresnel lens and falling on the back surface of a flat plate of having a thickness t, and a light ray leaving the front surface of the flat plate. As shown in FIG. 9, light rays obliquely falling on a convex lens 2 (a lens on the back surface) of a lenticular lens sheet 1 are not focused on a single point because those light rays are subject to aberration, and the light rays leave the front surface from a region having a width in the front surface. Accordingly, only a positional difference from a light ray a.sub.0 falling on the top of the convex lens 2 can be calculated by the foregoing expression. As is apparent from the tracking of the path of the light ray a.sub.0, the light ray a.sub.0 leaves the front surface of the lenticular lens sheet at a position at one end of a range having a width in which the light rays are distributed due to aberration. If a lens 3 on the front surface is substantially flat, the light ray a.sub.0 leaving the lens 3 travels in a direction substantially normal to the front surface. A light ray a.sub.1 falling on the lens 2 on the back surface at a position at one end of the lens 2 intersects a region on the lens 3 on the front surface at one end of the region corresponding to the other end of the lens 2 and leaves the lens 3 in a direction at a large angle to a normal to the surface of the lens 3. Therefore, at least the light rays falling on one end of the lens 2 or the light rays falling oh the other end of the lens 2 are trapped by the elevated section 5 if the BS ratio is increased without changing the positional difference, which reduces the viewing angle of the lenticular lens sheet when used as a display screen.